Present paper deals with applications of asymptotic equivalence relations on operator nets. These relations are defined via unbounded convergences on vector lattices. Given two convergences c and d on a vector lattice, we study d-asymptotic properties of operator nets formed by c-continuous operators. Asymptotic equivalences are known to be useful and extremely important tools to study infinite behaviors of strongly convergent operator nets and continuous semigroups. After giving a general theory, paper focuses on d-martingale and d-Lotz–Räbiger nets.